M-estimation and Median of Means applied to statistical learning

The main objective of this thesis is to study methods for robust statistical learning. Traditionally, in statistics we use models or simplifying assumptions that allow us to represent the real world. However, some deviations from the hypotheses can strongly disrupt the statistical analysis of a database. By robust statistics, we mean methods that can handle on the one hand so-called abnormal data (sensor error, human error) but also data of a highly variable nature. We apply robust techniques to statistical learning, giving theoretical efficiency results of the proposed methods as well as illustrations on simulated and real data.